Frequency Analysis of a Cable with Variable Tension and Variable Rotational Speed

Abstract

In this paper coupled nonlinear equations of motion of a suspended cable with time dependent tension and velocity are derived by using Hamilton's principal. A modal analysis for a stationary sagged cable is initially carried out in order to identify the dynamic system. The natural solution is directed to compute the natural frequencies and mode shapes of the free vibration of a suspended cable. Natural frequencies and mode shapes are plotted versus a dimensionless parameter l, known as static sag character. In case of moving cable, the tension force and the rotary speed of the pullies are assumed to be sinusoidal functions. Galerkin mode summation approach is utilized to discretize the nonlinear equations of motions. Numerical simulations are carried out in the time domain. A frequency analysis is then carried out and effects of the frequency of tension force and rotary speed on the belt dynamic responses are studied.